The purpose of this project is to improve the remission induction rate of acute lymphocytic leukemia in adult patients utilizing vincristine and dexamethasone with intermittent moderate doses of methotrexate followed by L'asparaginase. The second objective is to determine whether intermittent high dose methotrexate with leucovorum rescue and with vincristine and dexamethasone will prolong remission duration. The third objective is to determine the efficacy of moderate and high dose methotrexate in preventing meningeal leukemia and to correlate the clinical effectiveness with the cerebral spinal fluid methotrexate levels. To date, no previously untreated patients have been entered onto this study. Five previously treated patients have been entered on the study. Two patients achieved a complete remission after one course, one patient obtained a partial remission after three courses, and two patients are too early to evaluate (they both have started their first course of therapy).